Quantum Field Theory in a Nutshell:Second EditionA. Zee

You were born in China, educated in Brazil, pursued your undergraduate degree at Princeton, and then your Ph.D. at Harvard. . . . When did you first realize that you wanted to be a scientist--and, a physicist, in particular--as your profession in life?

When my family emigrated from Hong Kong to Brazil, we went by boat around the tip of Africa. The journey lasted for some 50 days, with stops at various ports along the way. What an eye-opening and formative experience for me! I recommend it to any kid. Back in those days we had the opposite of the information overflow we have today, and my mother was not sure when and if my schooling would resume, so she bought a pile of junior high or high school level textbooks for me to read in Brazil. I had lots of fun on the ship with my brothers and sister and newfound friends, but the moment I opened the physics book I was hooked. In hindsight, the book was terrible by modern pedagogical standards. The great physicist Murray Gell-Mann recalled how he hated physics as it was taught to him: all about memorizing "the 7 kinds of simple machines" and stuff like that. The book I devoured on the boat belonged to that category: I remember reading about the lever and the pulley. But in fact I was amazed that they worked because of a fundamental principle, that of energy conservation. I learned that, even behind everyday phenomena, there is something profound.

I have benefitted from good fortune all my life. One piece of good fortune is that the apartment my father had rented in the humongous city of Sao Paulo was by pure coincidence within walking distance of the American consulate. I soon discovered that the US Information Service maintained a library there. I still remember reading a book about how to manage a forest commercially, the different kinds of trees, when to cut them down, that sort of thing. It was wonderful that I was not confined in some school and tied to some specific curriculum and that I could read whatever interested me. Decades later, after I wrote Fearful Symmetry, somebody from the State Department asked me to represent the United States at a symmetry festival at the Center for the Performing Arts in Mumbai. I was more than happy to do so, paying back in some small way. The USIS shipped a pile of my book to India, and I joked that I finally learned how American foreign aid worked.

Later, after my father got his business in order, I went to an American school, and some of the teaching nuns had the good sense of excusing me from sitting in class for certain subjects. I was sent to the library. It was not much more than a large room with a small collection of books, but sitting there alone, surrounded by all that knowledge, was wonderful. I have a vivid image of coming across a book on linear algebra and reading about matrices.

Who were your intellectual and personal heroes as you were growing in your studies and profession? Who inspired and mentored you? Who was your best teacher?

A friend of mine somehow had a Russian book about puzzles in physics and math, which fascinated me to no end. (I still admire how the Russians train their physicists.) My memory is hazy, but somewhere, somehow, I also came across a popular book by George Gamow (to whom I paid homage when I wrote An Old Manís Toy/Einsteinís Universe.) He said that according to a certain professor John Wheeler at Princeton University, the atomic nucleus could take on different shapes, including that of a doughnut. That really motivated me to go to Princeton and find out from this Wheeler about this doughnut nucleus.

Among my many pieces of good fortune is that Princeton gave me a full scholarship. Perhaps I said on my application that I wanted to find out about the doughnut nucleus, but more likely the American nuns wrote strong letters about me. In response to a recent article in Physics Today about Wheelerís influence on various physicists, I wrote how Wheeler always made students feel important. In my sophomore year, he suggested that I calculate the emission of gravitational wave from a rotating neutron star. Even at that age I realized that I was merely plugging in numbers into the appropriate formulas in Landau and Lifschitz, but, whenever I showed Wheeler my calculation, he would be literally wild with excitement, heaping on praise and encouragement. Before I knew it, there appeared a manuscript by Zee and Wheeler. What would have been my first physics paper was, however, never published (but referred to as "to be published" in a long review article Wheeler later wrote), perhaps partly because Murph Goldberger and Sam Treiman (who would both mentor and influence me many years later, each in his characteristic way) decided to "rescue me from relativity" and point me towards particle theory. I immediately lost interest in gravitational waves and wanted to know about quantum field theory instead. By the way, Wheeler was quite gracious about my "escape from relativity" and even arranged for me to go to Harvard to work with Steve Weinberg, about whom he raved to me. As it happened, I did not end up working for Steve, but, many years later, when I visited Texas, he got me into writing popular-level books.

When did you first encounter quantum field theory? What is your own story of how you first came to understand quantum field theory? From whom/what book did you learn the subject? What was your first reaction to the subject?

For reasons that now escape me, I went from John Wheeler to Arthur Wightman who told me about exactly solvable field theory in 2-dimensional spacetime. (For reasons I did not appreciate at the time, the move did not please Goldberger.) At his suggestion, I spent a hot humid summer in Princeton reading the massive and not entirely coherent book by Schweber on quantum field theory. In the fall, I went to Wightman and asked him what book I should read next, he answered, "Read Schweber again." Wightman is a very kind and patient man (I remember standing there wondering why he was willing to spend so much time on me as he carefully explained some elementary point about quantum field theory on the blackboard), given to cryptic pronouncements. He once said to me something like "Football is algebraic, while basketball is geometric." I have been thinking about this ever since.

What is quantum field theory, anyway? How would you describe it to the person sitting next to you on an airplane?

Funny you should ask. Recently I flew back from Indiana University, where I gave a colloquium about quantum field theory, and I was thinking about this upcoming interview. During the entire flight the man sitting next to me was watching some violent war movie on his laptop. I didnít think he would be thrilled if I described to him what was on the first page of my book.

When did you first switch roles, from student to teacher? What subject did you teach?

As a matter of fact, the first course I ever taught as a beginning assistant professor at Princeton was quantum field theory.

When did you first teach QFT to students? What was your experience?

The most striking experience I now associate with the first time I taught quantum field theory? As I described on page xvii in the preface to the first edition of my book, I was amazed by the extraordinary quality of the solutions to the homework problems written up by my teaching assistant. His name? Ed Witten.

Do you notice that students ask the same kinds of questions you did, or do students ever surprise or challenge you with the questions they ask?

On page 454 I told the story that, when I took Schwingerís field theory course (which the better students at Harvard sat in on, year after year), the students understood that they were not allowed to ask questions. More seriously, I think that, to teach well and to write a good textbook, one has to be able to anticipate the questions to some extent. It is a form of empathy, the ability to put oneself in the mental framework of a typical student or reader. Many theoretical physicists fall into the trap of assuming that the typical student is like a typical denizen of their world.

How has your method of teaching this subject changed over the years? How do you clarify some of the most difficult concepts to students?

Most people, even physicists, do not realize that the last few decades have been a golden age of quantum field theory. The subject made enormous progress, with one triumph after another leading to "a victory parade that made the spectator gasp with awe and laugh with joy," to quote my thesis advisor Sidney Coleman (see page 473). Thus, my book is definitely not based on my lecture notes for the course on quantum field theory I alluded to above, from when I first taught the subject. Indeed, people should be warned that portions of various classic field theory texts have long gone out of date or are downright misleading.

What inspired you to write books? When did you decide to write a book? When did you decide that you wanted to attempt to explain the subject of QFT "in a nutshell"?

During that visit to Texas, I mentioned to Weinberg that for some years I had been urged to write up the notes of the class I gave when I first taught. He suggested writing a popular-level book instead, and that was the origin of Fearful Symmetry which I first published some 25 years ago and which Princeton now publishes. I knew that I still wanted to write a textbook eventually. The discussion started when the late Sam Treiman (also mentioned above) was on your board. As is clear to my readers, and as I explained in the two prefaces, I wanted to emphasize the profound concepts of quantum field theory more, and the formalism and computational techniques less. The latter are important, of course, but there are, alas, too many theoretical physicists walking around who can calculate without grasping the concepts. Unfortunately, our educational system fosters computational prowess since that is mostly what homework problems are about. One could hardly test for original thinking on a final exam. Thatís why some of the exercises in my book are open-ended, which, of course, throws the students in my course for a loop. They do not know to cope with an exercise asking for something other than plugging in the appropriate formula.

What was most challenging about writing this particular book? What was most satisfying in the end?

Writing a text in quantum field theory poses many challenges, of course. One of them is simply knowing when to stop. The subject is simply too rich, so there is bound to be complaints that I left out this or that topic (amidst complaints also that the book is too thick.) The satisfaction and challenges in writing a textbook and a popular-level book are completely different. In my popular-level books, such as Fearful Symmetry, I tried to convey to the reader, through vivid analogies and imageries, a flavor of what drives fundamental physics. In writing a textbook, I feel that, at the risk of sounding corny, I am passing on something to the next generation. I am expressing my gratitude to those who invented quantum field theory and to those who taught me quantum field theory, as I explained in more detail in the two prefaces. My hope is, of course, that--if Iím lucky--some readers of my book will be among those who will push quantum field theory forward. As I mentioned in the second edition, this has already happened since the first edition came out: I have already met some dashing young physicists who told me that they studied the subject from my book. The positive response of readers and of the physics community at large has been gratifying and makes the drudgery of actually writing the book worthwhile.

How do you feel your book explains this subject better or differently than other books?

I already touched upon this in #9. Every textbook writer has, or at least should have, a personality. I admire Weinberg profusely (and almost became his student, as I said), but his books are not what I could, or would want to, write. I prefer a lighter touch, with anecdotes and fictitious characters. My favorite is Confusio. Isnít he yours, too?

What other books are you working on?

After the gratifying success of my quantum field theory book, I decided to work on another textbook, titled Einstein Gravity in a Nutshell. In some sense, I am now writing about the second most beautiful subject in theoretical physics after quantum field theory. The book is written in the same style as my quantum field theory book, with the same light touch. Even Confusio is making a return appearance. In comparison to 10 years ago, I find myself more willing to fill in the gaps. As I write, I also keep shifting the book towards the more introductory end, so that I now start with a review of Newtonian mechanics and the action principle. I feel that it is important for students to get the foundation right rather than to master every technical detail. But I also consciously try not to "dumb down" the book (even though thatís surely the best way to increase sales.) Accessible and elementary are two different things. Einstein gravity, like quantum field theory, is a rich subject, and one difficulty for me is to know when to stop.

Do you feel that book writing helps you to look at subjects afresh or differently? Do you seek to inspire others with your books? What did you learn by writing this book?

The answers to the first two questions are absolutely and absolutely. In answering the third question I am afraid that I might get into my pet peeve: namely, that you canít please everyone, as I quoted Ricky Nelson in the preface of the book as saying. For example, in looking over my teaching evaluations, I read one studentís complaint that I donít do enough calculations in the course. But, my decades of teaching experience as my guide, this very same student, or others of his type, would surely complain that he is not getting enough concepts if the professor were to cover the board with long calculations. Sometimes I donít understand the weaker students in my course. By the time you get so far as to take quantum field theory, you should be all fired up about the beauty of theoretical physics; it should be a passion, a way of life. If you donít care about the subtlety and beauty of the concepts, but want to shut yourself in a cell calculating for the rest of your life, then you might have chosen the wrong profession to go into. You should be gasping with awe and laughing with joy. If not, do something else.

What do you think is the most important lesson for physics students to learn, if they want to become successful, professional physicists? What do you wish you would have learned earlier on in your studies?

I often asked my class, "What are you waiting for?" Are you waiting for a piece of paper before you start solving some of the great mysteries of theoretical physics at the most fundamental level? The leading physics journals actually do not ask to see a photostat of your diploma before they accept your paper. Did Newton wait? Did Schwinger wait? Did Dirac wait? The sad truth is that, if you spend your time worrying about getting through the homework and about acing the final exam, you probably wonít make it to the top level anyway. So, think more, and let your youthful creativity flow. You donít have to become an expert first. Indeed, by the time some people become experts, they are dead, or living but calcified.

In fact, I am rather reluctant to give advice to young theorists unless I know that person well. With so many different personality types, advice that would work for one kind of person would surely not be beneficial to another. Perhaps I could say this. If you are all fired-up about theoretical physics, make two lists. On the first list are problems that, if you solve one of them, could land you a job at a respectable university. On the second list are problems that, if you solve one of them, would have people dancing in the street. A former postdoc still sends me a email every time he publishes a paper, to ask me if people are dancing in Santa Barbara. The sad reality is that young people need to spend most of their time on the first list to get ahead and survive.

What in particular inspires you about quantum field theory? One published review of your book commented, "The purpose of Zee's book is not to turn students into experts--it is to make them fall in love with the subject. And Zee succeeds brilliantly." What is so beautiful about the subject that people seem to fall in love with it upon reading your book--as attested to by the glowing comments on amazon.com?

In my book, Fearful Symmetry, I tried very hard to convey the notion of beauty in physics. This is hard, because even I would find it unconvincing to state that elementary physics, particularly the way it is taught, is beautiful. To fundamental physicists, beauty is associated with elegance and simplicity, and simplicity means symmetry. Simple, however, does not mean simple-minded. To us fundamental physicists, simple and profound are closely linked. I would go so far as to say that the truly profound statements I know in fundamental physics are almost laughably simple, once you grasp them. But, of course, you canít grasp them unless you know the language. A rough analogy is perhaps a great poem that makes you see things in a simple way, but in order to see, you would have to experience life first. Another analogy is that, to read the poem, you have to know the language the poem is written in; and so, a physics textbook at the level of quantum field theory, which focuses on technical details, is like a book on poetry that spends hundred of pages explaining how the letters of the alphabet came about or how to write in different scripts. The most profound truths in physics are the most obvious, but of course they are only obvious in hindsight.